The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423036" target="_blank" >RIV/00216208:11320/20:10423036 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6zYxXcsT05" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6zYxXcsT05</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40315-020-00322-z" target="_blank" >10.1007/s40315-020-00322-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis

Popis výsledku v původním jazyce

As is the case for the theory of holomorphic functions in the complex plane, the Cauchy Integral Formula has proven to be a cornerstone of Clifford analysis, the monogenic function theory in higher dimensional euclidean space. In recent years, several new branches of Clifford analysis have emerged. Similarly as to how hermitian Clifford analysis in euclidean space R^2n of even dimension emerged as a refinement of euclidean Clifford analysis by introducing a complex structure on R^2n, quaternionic Clifford analysis arose as a further refinement by introducing a so-called hypercomplex structure Q, i.e. three complex structures (I, J, K) which follow the quaternionic multiplication rules, on R^4p, the dimension now being a fourfold. Two, respectively four, differential operators lead to first order systems invariant under the action of the respective symmetry groups U(n) and Sp(p). Their simultaneous null solutions are called hermitianmonogenic and quaternionicmonogenic functions respectively. In this contribution we further elaborate on the Cauchy Integral Formula for hermitian and quaternionic monogenic functions. Moreover we establish Caychy integral formulae for osp(4|2)-monogenic functions, the newest branch of Clifford analysis refining quaternionic monogenicity by taking the underlying symplectic symmetry fully into account.

Název v anglickém jazyce

The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis

Popis výsledku anglicky

As is the case for the theory of holomorphic functions in the complex plane, the Cauchy Integral Formula has proven to be a cornerstone of Clifford analysis, the monogenic function theory in higher dimensional euclidean space. In recent years, several new branches of Clifford analysis have emerged. Similarly as to how hermitian Clifford analysis in euclidean space R^2n of even dimension emerged as a refinement of euclidean Clifford analysis by introducing a complex structure on R^2n, quaternionic Clifford analysis arose as a further refinement by introducing a so-called hypercomplex structure Q, i.e. three complex structures (I, J, K) which follow the quaternionic multiplication rules, on R^4p, the dimension now being a fourfold. Two, respectively four, differential operators lead to first order systems invariant under the action of the respective symmetry groups U(n) and Sp(p). Their simultaneous null solutions are called hermitianmonogenic and quaternionicmonogenic functions respectively. In this contribution we further elaborate on the Cauchy Integral Formula for hermitian and quaternionic monogenic functions. Moreover we establish Caychy integral formulae for osp(4|2)-monogenic functions, the newest branch of Clifford analysis refining quaternionic monogenicity by taking the underlying symplectic symmetry fully into account.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-11473S" target="_blank" >GA20-11473S: Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computational Methods and Function Theory

ISSN

1617-9447

e-ISSN

—

Svazek periodika

20

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

34

Strana od-do

431-464

Kód UT WoS článku

000542081500001

EID výsledku v databázi Scopus

2-s2.0-85086777972